{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AOWHKJKEVXBC4YBELUL7OJWLOK","short_pith_number":"pith:AOWHKJKE","canonical_record":{"source":{"id":"1608.05849","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-20T17:01:10Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"1e8c6af849651668dc7af81ab508ee58460d8a164f0d3dabb58bd34cf93b53ac","abstract_canon_sha256":"5cb2dd30e90afa135ef6171ed382b9f7f14c9699125efcc5b7291c9c8f1a1a3c"},"schema_version":"1.0"},"canonical_sha256":"03ac752544adc22e60245d17f726cb72a2ef7bc53e04aa84c1ad9f12aedbb253","source":{"kind":"arxiv","id":"1608.05849","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05849","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05849v3","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05849","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"pith_short_12","alias_value":"AOWHKJKEVXBC","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AOWHKJKEVXBC4YBE","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AOWHKJKE","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AOWHKJKEVXBC4YBELUL7OJWLOK","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05849","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-20T17:01:10Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"1e8c6af849651668dc7af81ab508ee58460d8a164f0d3dabb58bd34cf93b53ac","abstract_canon_sha256":"5cb2dd30e90afa135ef6171ed382b9f7f14c9699125efcc5b7291c9c8f1a1a3c"},"schema_version":"1.0"},"canonical_sha256":"03ac752544adc22e60245d17f726cb72a2ef7bc53e04aa84c1ad9f12aedbb253","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:08.021711Z","signature_b64":"yCGq5e8buiThP9eJf2iqZSblJEomjhNY0Khx5oyRvV7O2tWcnPB1ONY+vxJEBPz1Fma+6mMgJ2MDlnNc1eF3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03ac752544adc22e60245d17f726cb72a2ef7bc53e04aa84c1ad9f12aedbb253","last_reissued_at":"2026-05-18T00:46:08.021248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:08.021248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05849","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+3wR2IunsnpnMloAjCCw2hjlbpC8lyGU0yBuk4CMlCLNCArOHioiIs+rQNJRPGOUTCWISrkHgtuYHBeOdg5lDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T15:24:27.767657Z"},"content_sha256":"85d732d535fe78f6837309ea5958c0d59d4e7b516211bb3a4c3d278a0936954d","schema_version":"1.0","event_id":"sha256:85d732d535fe78f6837309ea5958c0d59d4e7b516211bb3a4c3d278a0936954d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AOWHKJKEVXBC4YBELUL7OJWLOK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bound for preperiodic points for maps with good reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Sebastian Troncoso","submitted_at":"2016-08-20T17:01:10Z","abstract_excerpt":"Let $K$ be a number field and let $\\phi$ in $K(z)$ be a rational function of degree $d\\geq 2$. Let $S$ be the places of bad reduction for $\\phi$ (including the archimedan places). Let $Per(\\phi,K)$, $PrePer(\\phi, K)$, and $Tail(\\phi,K)$ be the set of $K$-rational periodic, preperiodic, and purely preperiodic points of $\\phi$, respectively. The present paper presents two main results. The first result gives a bound for $|PrePer(\\phi,K)|$ in terms of the number of places of bad reduction $|S|$ and the degree $d$ of the rational function $\\phi$. This bound significantly improves a previous bound "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05849","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"by35HfI0L0yoG9CDSnA1sE4lzx7KbDh4iseebRPcE7vrjuu1kaCVt4lTzbYXFmmMasf49VfjV2D29s++4s1OBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T15:24:27.768000Z"},"content_sha256":"0f6f4ac8b5e937df7b44073bd73419aaa5985ba6d7301ea288797b5292f2bcab","schema_version":"1.0","event_id":"sha256:0f6f4ac8b5e937df7b44073bd73419aaa5985ba6d7301ea288797b5292f2bcab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AOWHKJKEVXBC4YBELUL7OJWLOK/bundle.json","state_url":"https://pith.science/pith/AOWHKJKEVXBC4YBELUL7OJWLOK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AOWHKJKEVXBC4YBELUL7OJWLOK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T15:24:27Z","links":{"resolver":"https://pith.science/pith/AOWHKJKEVXBC4YBELUL7OJWLOK","bundle":"https://pith.science/pith/AOWHKJKEVXBC4YBELUL7OJWLOK/bundle.json","state":"https://pith.science/pith/AOWHKJKEVXBC4YBELUL7OJWLOK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AOWHKJKEVXBC4YBELUL7OJWLOK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AOWHKJKEVXBC4YBELUL7OJWLOK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5cb2dd30e90afa135ef6171ed382b9f7f14c9699125efcc5b7291c9c8f1a1a3c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-20T17:01:10Z","title_canon_sha256":"1e8c6af849651668dc7af81ab508ee58460d8a164f0d3dabb58bd34cf93b53ac"},"schema_version":"1.0","source":{"id":"1608.05849","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05849","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05849v3","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05849","created_at":"2026-05-18T00:46:08Z"},{"alias_kind":"pith_short_12","alias_value":"AOWHKJKEVXBC","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AOWHKJKEVXBC4YBE","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AOWHKJKE","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:0f6f4ac8b5e937df7b44073bd73419aaa5985ba6d7301ea288797b5292f2bcab","target":"graph","created_at":"2026-05-18T00:46:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $K$ be a number field and let $\\phi$ in $K(z)$ be a rational function of degree $d\\geq 2$. Let $S$ be the places of bad reduction for $\\phi$ (including the archimedan places). Let $Per(\\phi,K)$, $PrePer(\\phi, K)$, and $Tail(\\phi,K)$ be the set of $K$-rational periodic, preperiodic, and purely preperiodic points of $\\phi$, respectively. The present paper presents two main results. The first result gives a bound for $|PrePer(\\phi,K)|$ in terms of the number of places of bad reduction $|S|$ and the degree $d$ of the rational function $\\phi$. This bound significantly improves a previous bound ","authors_text":"Sebastian Troncoso","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-20T17:01:10Z","title":"Bound for preperiodic points for maps with good reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05849","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:85d732d535fe78f6837309ea5958c0d59d4e7b516211bb3a4c3d278a0936954d","target":"record","created_at":"2026-05-18T00:46:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5cb2dd30e90afa135ef6171ed382b9f7f14c9699125efcc5b7291c9c8f1a1a3c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-20T17:01:10Z","title_canon_sha256":"1e8c6af849651668dc7af81ab508ee58460d8a164f0d3dabb58bd34cf93b53ac"},"schema_version":"1.0","source":{"id":"1608.05849","kind":"arxiv","version":3}},"canonical_sha256":"03ac752544adc22e60245d17f726cb72a2ef7bc53e04aa84c1ad9f12aedbb253","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03ac752544adc22e60245d17f726cb72a2ef7bc53e04aa84c1ad9f12aedbb253","first_computed_at":"2026-05-18T00:46:08.021248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:08.021248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yCGq5e8buiThP9eJf2iqZSblJEomjhNY0Khx5oyRvV7O2tWcnPB1ONY+vxJEBPz1Fma+6mMgJ2MDlnNc1eF3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:08.021711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05849","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85d732d535fe78f6837309ea5958c0d59d4e7b516211bb3a4c3d278a0936954d","sha256:0f6f4ac8b5e937df7b44073bd73419aaa5985ba6d7301ea288797b5292f2bcab"],"state_sha256":"94bc6e7c6a6e924ca414d891d98a519bb13bbd1f0e2d2de632ace4b696a54d28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VJCzDQGPPLQAlHSFZ9AE5/88jvcxFEbcISexQLEpEKFvadtaW5Sv6Reg1qw5ufloMiok7bAVF8MtEjdjSibKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T15:24:27.770611Z","bundle_sha256":"0df9318bed7ce1e1f43959a8cfebaf0f225d9bbe870e4032443ad858b16cb60f"}}